2010015605

The rectangular box $ABCD{A}^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }$ has edges of lengths $|AB|=6\mathrm{cm}$ and $|BC|=8\mathrm{cm}$. The point $S$ is the center of the base $ABCD$ (see the picture) and the length of the line segment $A^{\prime }S$ is $13\mathrm{cm}$. Find the distance between the points $A$ and $A^{\prime }$.